Squares in (2^2-1)...(n^2-1) and p-adic valuation

Abstract

In this paper, we determine all the squares in the sequence $\{{\prod }_{k=2}^n(k^2-1){\}}_{n=2}^{\infty }$. From this, one deduces that there are infinitely many squares in this sequence. We also give a formula for the $p$-adic valuation of the terms in this sequence.

4 pages. To appear in Asian-European J. Math